As the requirement for data rate for optical communications increases, newer coded modulations are required to achieve low bit-error rate (BER), to increase data rates, fiber distance, and spectral density. For optical communications, as the data rate increases, more complicated quadrature-amplitude modulation (QAM) formats, such as 8QAM, 16QAM, 64QAM, 256QAM, 1024QAM, etc., are generated. These modulations typically have varying signal power depending on the symbols, and can cause phase noise on the signal a channel as well as other wavelength-division multiplexed channels. While phase-shift keying (PSK) modulation formats have constant modulus at each symbol timing, the BER performance can seriously degrade compared to QAM because of the shorter constellation distance.
For example, 8-ary QAM (8QAM) plays an important role by filling the gap between quaternary PSK (QPSK) and 16QAM in terms of bit rates and fiber distance. It has also been proposed that hybrid QAMs such as 8QAM-16QAM or QPSK-8QAM used in time-domain.
In order to achieve similar bit rates with improved sensitivity, quaternary codes, spherical lattice-cut codes, and 4D honeycomb lattice codes can be used. However, for these 6 bits/symbol codes, achieving high sensitivity, Gray coding, and constant modulus at the same time has not been realized.
In WO 2009/124861 “Modulation scheme with increased number of states of polarizations,” the number of states of polarization is increased using a Stokes space as a guide. However, how the states of polarization can be optimized using the existing sets of polarizations is not described.
Pi/4-shift QPSK modulation achieves lower power envelope fluctuation during symbol transition, and generates a reasonably constant modulus waveform. Minimum shift keying (MSK) and frequency-shift keying (FSK) can generate perfectly constant modulus waveforms even in-between symbol transitions. However, there is no MSK/FSK achieving high data rates because the increased number of cardinalities expands the required bandwidth. And, it does not exploit 4D optical carrier fields. Trellis shaping is known as another method of generating constant modulus signals. However, this technique requires additional overhead and complexity for trellis coding.